Efficient block-coordinate descent algorithms for the Group Lasso

Mathematical Programming Computation - Tập 5 Số 2 - Trang 143-169 - 2013
Zhiwei Qin1, Katya Scheinberg2, Donald Goldfarb1
1Department of Industrial Engineering and Operations Research, Columbia University, New York, USA#TAB#
2Department of Industrial and Systems Engineering, Lehigh University, Bethlehem, USA

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Tài liệu tham khảo

Bach, F.: Consistency of the group Lasso and multiple kernel learning. J. Mach. Learn. Res. 9, 1179–1225 (2008)

Beck, A., Teboulle, M.: A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imag. Sci. 2(1), 183–202 (2009)

van den Berg, E., Friedlander, M.: Joint-sparse recovery from multiple measurements. arXiv 904 (2009)

van den Berg, E., Friedlander, M.: Sparse Optimization With Least-squares Constraints. Tech. rep., Technical Report TR-2010-02, Department of Computer Science, University of British Columbia, Columbia (2010)

van den Berg, E., Schmidt, M., Friedlander, M., Murphy, K.: Group sparsity via linear-time projection. Tech. rep., Technical Report TR-2008-09, Department of Computer Science, University of British Columbia, Columbia (2008)

Candès, E., Romberg, J., Tao, T.: Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. Inform Theory IEEE Trans 52(2), 489–509 (2006)

Chen, J., Huo, X.: Theoretical results on sparse representations of multiple-measurement vectors. IEEE Trans. Signal Process. 54, 12 (2006)

Dolan, E., Moré, J.: Benchmarking optimization software with performance profiles. Math. Program. 91(2), 201–213 (2002)

Donoho, D.: Compressed sensing, information theory. IEEE Trans. 52(4), 1289–1306 (2006)

Friedman, J., Hastie, T., Tibshirani, R.: A note on the group lasso and a sparse group lasso. preprint, Leipzig (2010)

Jacob, L., Obozinski, G., Vert, J.: Group Lasso with overlap and graph Lasso. In: Proceedings of the 26th Annual International Conference on Machine Learning, ACM, New York, pp. 433–440 (2009)

Kim, D., Sra, S., Dhillon, I.: A scalable trust-region algorithm with application to mixed-norm regression. vol. 1. In: Internetional Conference Machine Learning (ICML), Atlanta (2010)

Kim, S., Xing, E.: Tree-guided group lasso for multi-task regression with structured sparsity. In: Proceedings of the 27th Annual International Conference on, Machine Learning, New York (2010)

Liu, J., Ji, S., Ye, J.: Multi-task feature learning via efficient l 2, 1-norm minimization. In: Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence, AUAI Press, Corvallis, pp. 339–348 (2009)

Liu, J., Ji, S., Ye, J.: SLEP: Sparse Learning with Efficient Projections. Arizona State University, Arizona (2009)

Ma, S., Song, X., Huang, J.: Supervised group Lasso with applications to microarray data analysis. BMC bioinformatics 8(1), 60 (2007)

Meier, L., Van De Geer, S., Buhlmann, P.: The group lasso for logistic regression. J. Royal Stat. Soc. Ser. B (Stat. Methodol.) 70(1), 53–71 (2008)

Moré, J., Sorensen, D.: Computing a trust region step. SIAM J. Sci. Statist. Comput. 4, 553 (1983)

Nesterov, Y.: Efficiency of coordinate descent methods on huge-scale optimization problems. CORE Discussion Papers, Belgique (2010)

Nocedal, J., Wright, S.: Numerical optimization. Springer verlag, New York (1999)

Rakotomamonjy, A.: Surveying and comparing simultaneous sparse approximation (or group-lasso) algorithms. Sig. Process. 91(7), 1505–1526 (2011)

Richtárik, P., Takáč, M.: Iteration complexity of randomized block-coordinate descent methods for minimizing a composite function. Arxiv, preprint arXiv:1107.2848 (2011)

Roth, V., Fischer, B.: The group-lasso for generalized linear models: uniqueness of solutions and efficient algorithms. In: Proceedings of the 25th international conference on Machine learning, ACM, Bellevue, pp. 848–855 (2008)

Subramanian, A., Tamayo, P., Mootha, V., Mukherjee, S., Ebert, B., Gillette, M., Paulovich, A., Pomeroy, S., Golub, T., Lander, E., et al.: Gene set enrichment analysis: a knowledge-based approach for interpreting genome-wide expression profiles. Proc. Natl Acad. Sci. U.S.A. 102(43), 15,545 (2005)

Sun, L., Liu, J., Chen, J., Ye, J.: Efficient Recovery of Jointly Sparse Vectors. NIPS, Canada, (2009)

R, Tibshirani: Regression shrinkage and selection via the lasso. J. Royal Statist. Soc. Ser. B (Methodol.) 58(1), 267–288 (1966)

Tseng, P.: Convergence of a block coordinate descent method for nondifferentiable minimization. J. Optim. Theory Appl. 109(3), 475–494 (2001)

Tseng, P., Yun, S.: A coordinate gradient descent method for nonsmooth separable minimization. Math. Program. 117(1), 387–423 (2009)

Van De Vijver, M., He, Y., van’t Veer, L., Dai, H., Hart, A., Voskuil, D., Schreiber, G., Peterse, J., Roberts, C., Marton, M., et al.: A gene-expression signature as a predictor of survival in breast cancer. N. Engl. J. Med. 347(25), 1999 (2002)

Vandenberghe, L.: Gradient methods for nonsmooth problems. EE236C course notes (2008)

Wright, S., Nowak, R., Figueiredo, M.: Sparse reconstruction by separable approximation. IEEE Trans. Signal Process. 57(7), 2479–2493 (2009)

Yang, H., Xu, Z., King, I., Lyu, M.: Online learning for group lasso. In: 27th Intl Conf. on Machine Learning (ICML2010). Citeseer (2010)

Yuan, M., Lin, Y.: Model selection and estimation in regression with grouped variables. J. Royal Statist. Soc. Ser. B (Statist. Methodol.) 68(1), 49–67 (2006)

Zou, H., Hastie, T.: Regularization and variable selection via the elastic net. J. Royal Statist. Soc. Ser. B (Statist. Methodol.) 67(2), 301–320 (2005)